Greedy spanners are optimal in doubling metrics

Abstract

We show that the greedy spanner algorithm constructs a (1 + ∈)-spanner of weight ∈−O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [10]. Our result generalizes the result by Narasimhan and Smid [13] who showed that a point set in d-dimension Euclidean space has a (1+∈)-spanner of weight at most ∈−O(d)w(MST). Our proof only uses the packing property of doubling metrics and greatly simplifies the proof of the same result in Euclidean space.